Consider the following hypothesis test ;
$H_0 : \mu ≥20$
$H_1 : \mu < 20 $
A sample of 64 provided a sample mean of 19.5. The population standard deviation is 2. The value of the test statistic is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → -2
Sample size, $n=64$
Sample mean, $\bar x=19.5$
Population standard deviation, $σ=2$
Under $H_0$, we use $μ_0=20$
The test statistics,
$z=\frac{\bar x-μ_0}{σ/\sqrt{n}}=-\frac{0.5}{0.25}=-2$